Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn:   1^2 + 4^2 + 7^2 + . . . + (3n - 2)2 = n(6n^2-3n-1)/2

Answer 1

@jigglypuff314 could you help me

Answer 2

@Preetha can you help me?

Answer 3

So, you will replace n here with 1, 2, and 3 for each separate expression. When expanding in the form Sn: Notice that you only need to go as far as (3n - 2)2. Therefore, let's say you pick 2. This will only go as far as 4^2, so you discard the pattern after this.

Answer 4

Verify whatever solution you give is correct by both adding it the expanded Sn form, and in the equation on the right. They should be equal.

Answer 5

@unknownunknown i dont understand this what is the +...+ for

Answer 6

Let's imagine that n = 1 billion billion (1,000,000,000). It wants to show you the pattern to calculate it. the Sn: shows the first three terms, the ... (dot dot dot) represents the rest of the terms, and the end term (3n-2)^2 shows the last term.

It's a short hand notation to show that a series can be calculate by following the same pattern until some end term.

Answer 7

If we really had a billion terms, it would take forever to write the entire equation, right?